Ruby library that contains various mathematical functions and algorithms, extending Ruby's capabilities in domains such as statistics, numerical analysis, and combinatorics.

1. Mathematical Functions

   • Gamma Function: Computes the gamma function for real numbers.
   • Beta Function: Calculates the beta function and its regularized form.
   • Error Function (erf): Provides the error function used in probability and statistics.

2. Special Functions

   • Lambert W Function: Solves equations of the form x = a * exp(x).
   • Continued Fractions: Evaluates continued fractions for various mathematical expressions.

3. Statistical Tools

   • Probability Distributions: Implements distributions like Student's t, chi-squared, and Fisher's z.
   • Random Number Generation: Generates random numbers following specific distributions.
   • Hypothesis Testing: Performs tests like the Kolmogorov-Smirnov test for distribution comparison.

4. Sequence Analysis

   • Moving Averages: Computes simple moving averages for time series data.
   • Autocorrelation and Autovariance: Analyzes the correlation structure of sequences.
   • Histograms: Visualizes data distributions with customizable bins.

5. Combinatorics and Algorithms

   • Permutations and Combinations: Generates permutations, combinations, and Cartesian products.
   • Graph Theory: Includes algorithms for shortest paths (Dijkstra, Floyd-Warshall) and minimum spanning trees.
   • Root Finding: Uses Newton-Raphson and bisection methods to find roots of functions.

1. String Numeral Conversion

   • Converts strings to Gödel numbers and vice versa using a specified alphabet.

2. Cantor Pairing Function

   • Encodes tuples into a single integer and decodes them back, useful in set theory and combinatorics.

3. Histograms

   • Creates histograms for data visualization with support for different binning strategies.

include MoreMath::Functions # include like you would ::Math

# Compute the gamma function at 0.5
puts gamma(0.5) # => 1.77245385091

# Define a continued fraction representation of the arctangent function (atan)
atan = ContinuedFraction.for_a do |n, x|
  n == 0 ? 0 : 2 * n - 1
end.for_b do |n, x|
  n <= 1 ? x : ((n - 1) * x) ** 2
end
pi = -> (epsilon: 1E-16) { 4 * atan.(1, epsilon:) }
puts pi.() # => 3.1415926535897936

# Compute the moving average of an array
sequence = [1, 2, 3, 4, 5]
ma = Sequence.new(sequence).simple_moving_average(2)
puts ma.inspect # => [1.5, 2.5, 3.5, 4.5]

# Create a histogram with 3 bins, display it in on STDOUT with a width of 80 characters
Histogram.new([1, 2, 3, 4, 5, 1], bins: 3).display(STDOUT, 80) ; nil
#   4.33333 -|⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
#   3.00000 -|⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
#   1.66667 -|⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

To install more_math, run:

gem install more_math

Florian Frank
mailto:flori@ping.de

This software is licensed under the X11 (or MIT) license: http://www.xfree86.org/3.3.6/COPYRIGHT2.html#3

The homepage of this library is located at:

• http://github.com/flori/more_math